Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves
成果类型：
Article
署名作者：
Auroux, Denis; Katzarkov, Ludmil; Orlov, Dmitri
署名单位：
Massachusetts Institute of Technology (MIT); University of Miami; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-006-0003-4
发表日期：
2006
页码：
537-582
关键词：
摘要：
We study homological mirror symmetry for Del Pezzo surfaces and their mirror Landau-Ginzburg models. In particular, we show that the derived category of coherent sheaves on a Del Pezzo surface X-k obtained by blowing up CP2 at k points is equivalent to the derived category of vanishing cycles of a certain elliptic fibration W-k :M-k -> C with k+3 singular fibers, equipped with a suitable symplectic form. Moreover, we also show that this mirror correspondence between derived categories can be extended to noncommutative deformations of X-k , and give an explicit correspondence between the deformation parameters for X-k and the cohomology class [B+i omega]epsilon H-2 (M-k , C).
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